Thermal Engineering, Refrigeration & Power

For a circular cross-section of diameter $d$, the rectangular area moments of inertia about the centroidal axes are $I_{xx} = I_{yy} = \frac{\pi d^4}{64}$. By the Perpendicular Axis Theorem, the polar moment of inertia ($I_p$ or $J$) about an axis perpendicular to the plane of the circle is the sum of both orthogonal moments:

Option analysis:

• $\frac{\pi d^4}{64}$: Represents planar moment of inertia ($I_{xx}$ or $I_{yy}$), not polar moment.
• $\frac{\pi d^4}{32}$: Correct polar moment of inertia of a circular section.
• $\frac{\pi d^4}{16}$: Incorrect.
• $\frac{\pi d^3}{32}$: Represents polar section modulus ($Z_p$), not moment of inertia.

In alternating current (AC) circuit theory, when two sinusoidal quantities (such as voltage and current, or two voltages) have the identical frequency but pass through their corresponding zero points (or maximum values) at different instants of time, they are said to have a phase difference (or phase displacement $\phi$).

Option analysis:

• Current difference: General arithmetic difference in amperes.
• Phase difference: Correct, angular time displacement between waveforms of identical frequency.
• Zero difference: Non-standard phrase.
• Voltage difference: General potential difference in volts.